After leaving the sewers you're deposited just outside the Imperial City. From here you have a few options for your next step. If you want to deliver the amulet right away, use your map to quick travel to Weynon Priory. However, as urgent as the characters make it sound in-game, there's no rush. The main quest can be postponed as long as you like.

Getting There

Quick traveling is the fastest way to get there, but it can also be the least interesting. The quest system will display an arrow at the bottom of your screen, pointing you to the quest location. The arrow will be red when the target is inside a building (or outside if you're in one), or otherwise in a different location than you. If the arrow is green, this means your target is in the same area you are. Don't get too excited about this if your target is outside, since you can be anywhere outside and still be in the same area. Use the in-game map and arrow to keep going in the right direction. There are plenty of caves and other interesting locations to explore on the way and there's no time penalty, so take your time.

Option #2

Since you're right next to the Imperial City, a good first step would be to go and sell any items you've collected in the sewers that you don't need. The Imperial City is also a good place to start for fighter and thief type characters.

Thief

If you're a thief, then the Imperial City is the place to get your start in the Thieves Guild. The fastest way to do this is by stealing something and letting yourself get caught. After you're released from prison, someone will give you a note to get you started on your path to Thieves Guild membership.

Fighter

Fighters may be interested in the arena. It's a good way to earn some quick gold and start building up your skills. Just head over to the arena district, either on foot or via fast travel.

Other Quests

The Imperial City has a bunch of other freelance quests. Talk to everyone, and I do mean everyone. Talking to people can give you clues on finding treasure and quests. Two interesting quests can be found in the merchant and waterfront areas. In the merchant district, just talk to any of the shopkeepers to find out about some unfair competition. For the adventurous, go buy a room in the Bloated Float Inn, on the waterfront. Sleep in the bed downstairs, when you wake up, you'll be on a short adventure.